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A056093 Number of 5-element ordered antichain covers of an unlabeled n-element set. 4
30, 2176, 54036, 709956, 6290051, 42606671, 237197942, 1135834242, 4823607212, 18563958502, 65783057592, 217240417628, 674884181813, 1987124979703, 5579019610088, 15010371955248, 38862554420034, 97163223921924, 235290234202584, 553296290481584 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

REFERENCES

V. Jovovic, G. Kilibarda, On enumeration of the class of all monotone Boolean functions, in preparation.

LINKS

G. C. Greubel, Table of n, a(n) for n = 4..1000

K. S. Brown, Dedekind's problem

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, (English translation), Discrete Mathematics and Applications, 9, (1999), no. 6.

Eric Weisstein's World of Mathematics, Antichain covers

FORMULA

a(n)=C(n + 30, 30) - 20*C(n + 22, 22) + 60*C(n + 18, 18) + 20*C(n + 16, 16) + 10*C(n + 15, 15) - 110*C(n + 14, 14) - 120*C(n + 13, 13) + 150*C(n + 12, 12) + 120*C(n + 11, 11) - 240*C(n + 10, 10) + 20*C(n + 9, 9) + 240*C(n + 8, 8) + 40*C(n + 7, 7) - 205*C(n + 6, 6) + 60*C(n + 5, 5) - 210*C(n + 4, 4) + 210*C(n + 3, 3) + 50*C(n + 2, 2) - 100*C(n + 1, 1) + 24*C(n, 0).

MATHEMATICA

Table[Binomial[n+30, 30]-20 Binomial[n+22, 22]+60 Binomial[n+18, 18]+ 20 Binomial[n+16, 16]+ 10 Binomial[n+15, 15]-110 Binomial[n+14, 14]- 120 Binomial[n+13, 13]+ 150 Binomial[n+12, 12]+ 120 Binomial[n+11, 11]- 240 Binomial[n+10, 10]+ 20 Binomial[n+9, 9]+ 240 Binomial[n+8, 8]+ 40 Binomial[n+7, 7]- 205 Binomial[n+6, 6]+ 60 Binomial[n+5, 5]- 210 Binomial[n+4, 4]+ 210 Binomial[n+3, 3]+ 50 Binomial[n+2, 2]- 100 Binomial[n+1, 1]+ 24 Binomial[n, 0], {n, 4, 30}] (* Harvey P. Dale, Sep 06 2011 *)

CROSSREFS

Cf. A056048 for 5-antichain (unordered) covers of a labeled n-set, A051113. See also A056074, A056090.

Sequence in context: A255958 A092617 A295446 * A056070 A301377 A054647

Adjacent sequences:  A056090 A056091 A056092 * A056094 A056095 A056096

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Goran Kilibarda, Zoran Maksimovic, Jul 27 2000

EXTENSIONS

More terms from Harvey P. Dale, Sep 06 2011

STATUS

approved

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Last modified June 27 16:27 EDT 2022. Contains 354896 sequences. (Running on oeis4.)